This is a difficult question to answer because in a certain view of things, 'force' itself is fundamental, indeed, the sole fundamental property of reality apart from space itself: in other words, there is nothing more physically fundamental in terms of which 'force' may be defined. The idea therefore becomes descriptive. Indeed, in practice, there is no empirical context (nor any experimental context, in the case in which forces are expressly applied) which can be described analytically without either alluding to, inferring or explicitly invoking the idea of 'force'; as the OP suggests in reference to 'inertial frames', the essence of the concept simply cannot be expunged from scenarios of physical mechanics.
So, in exploring the fundamental nature of the very idea of 'force', it is perhaps instructive to consider the original opinion of Faraday in imagining the existence of a singular universal substance of which all reality is composed -- which in the ideation of his day required one to envisage no ultimate qualitative distinction between 'aether' and 'matter' -- that such a substance or universal fabric is or would be effectively indistinguishable from the correspondingly unitary fundamental force holding it together. While, as I recall, that view does not explicitly state its reasoning, it seems clear that such a practical constraint arises because the sole means of apprehending the nature of such a substance (for those such as we who are also comprised entirely of it) is through a mechanism of resonance between components of that force -- let us call it a 'cohesive force' -- comprising one's being and those components extrinsic to us in the exterior world.
Moreover, the very effect that a universal substance would be perceptible in such a way is inevitably due not merely to the disparity between these contexts, but to the further effect that such a substance must exist in a condition of perpetual inertia: in the following treatment of such a conception, not only does the state of alignment between components of the fundamental cohesive force tend to be maintained universally -- which is only to say that the condition of relative equilibrium between opposing components tends to be sustained --, but must from a philosophical standpoint tend inexorably towards increase.
To understand what is meant here by 'alignment' of such components, and its equivalence to a condition of 'cohesive resonance' between them, consider that in order to conceive the appropriate geometrical model of such a unitary universal substance based on the self-evident presumption that a unitary and exclusive fundamental 'cohesive force' inheres within it, it is first necessary to imply what amounts to a correspondingly unitary universal 'field' in which all points are in some degree of interaction with all others mediated solely by such a force. (Indeed, Faraday's conception of 'fields' is presumably that these represent the organisation of components of such a force and their integration in more-or-less recognisable ways in various contexts within the universal entity.).
As is evident, force imagined in such a fundamental way may be said to act only against itself, in an infinite array of disparate components distributed universally to the end of an ideal condition of ultimate equilibrium or cohesive symmetry; and it is this fundamental tendency which is equivalent to that of both an alignment between components of cohesive force, and in the case of opposing components, their state of relative equilibrium or 'cohesive equilibration: the two ideas are equivalent to that of 'resonance' between such components. It should be emphasised however that no true symmetry exists within this reality, only the inexorable proclivity towards such an idealised state.
Regarding any two loci in such a 'field' -- broadly a tensor/vector field --, it is self-evidently true that, since a condition of perfect equilibrium or symmetry between any such points implies immediate universal cessation, the cohesive interaction between them must be disparate: viz, a resultant in cohesive force or fundamental polarity must arise between them. At the same time, since it is the primary postulate of such a conception that all such interaction is the manifestation of a singular universal impetus towards such a state of cohesive equilibrium or symmetry, then the dynamic interaction between such disparate components of cohesive force may be modeled within a conceptual framework representing this ultimately idealised state of cohesive symmetry or equilibrium.
In order to represent this idealised state, one may immediately propose a cubic lattice-type model in which each cubic vertex in two interlocking reciprocal aspects represents such a locus of cohesive force; and in that conceptual context, the geometry of such a structure in which fundamental polarities or resultants in cohesive force are implied by the disparities between the 3 cubic dimensions (the pole, edge and face diagonal) -- thus 3 basic fundamental vectors of cohesive force arising at a common frequency -- permits the inference of a basic wave interference effect between these resultants (or fundamental vectors of cohesive polarity) whose dynamics of progression and recurrence with respect to the idealised lattice structure of 'cohesive symmetry' constitutes the basis on which a 'unitary universal cohesive field' may be modeled within which such a unitary oscillatory wave principle is inherent.
'Force' then in such a conception is truly fundamental; not only should the 4 'fundamental forces' of physics be understood as aspects of such a unitary universal force construed in varying contexts, but all other physical properties and quantities, energy and momentum in particular, are measures of the inter-relation between and integration of components of such a fundamental 'cohesive force'. Even 'charge' is postulated in this model as a radial component in the expanding plane of intersection between two opposing components of cohesive force operating in the cubic polar axis of the lattice model suggested.
That is, imagining such an interaction in mutual cohesion between disparate components as two intersecting spheres centred at points on an axis, a plane of distribution of that resultant force arising between them will expand from its point of origin orthogonal to that axis: a plane of 'cohesive tension' (curving towards the stronger locus of force); and it is in such planes that 'charge' is defined in this model. Moreover, it is this essential orthogonal relation between the cohesive force along a cubic axis and the plane of its distribution which is at the basis of orthogonality between electric and magnetic aspects of EM fields in the orthodox analysis, indeed, of all orthogonality between quantities and functions in the SM including complex functions.
For those curious about the potential value of such a conception and its model of a 'unitary universal (cohesive) force field', certain basic physical quantities and measures may be readily inferred from it, in particular, the neutron-proton and muon-electron mass ratios; a value for the range of visible light frequencies of dominant solar EMR when a specific temporal periodicity is imputed to the unitary universal oscillatory wave (interference) dynamic; the geometric basis for the 'fine structure constant', and the physical basis for Planck's constant. One may of course refuse to concede the premise itself of an effectively inviolate unitary universal entity, and of the concept of a correspondingly unitary 'universal substance or fabric', moreover to repudiate the logical corollaries of a unitary cohesive force, and the singular impetus towards an idealised state of symmetry between its components following from those premises -- in which case one will be left with the parlous state of orthodox physics and cosmology as it is, an engineering masterpiece to be sure, but quite incapable introspectively of addressing even the most fundamental of questions such as that posed here.
